References & Citations
Mathematics > Dynamical Systems
Title: Bowen's formula for a rational graph-directed Markov system
(Submitted on 27 Mar 2024)
Abstract: We establish Bowen's formula for the Julia set of a non-elementary, expanding, irreducible and aperiodic rational graph-directed Markov system satisfying the backward separating condition. Towards this end, we shall prove that the associated skew product map is topologically exact on the skew product Julia set, and satisfies the density of repelling periodic points. Moreover, we give a criterion for expandingness in terms of hyperbolicity.
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